Obviously, in the second scene, where Leela was cut by Fry, she meant to say, "Hey Fry, I know what you could penetrate." The irony was in Fry not getting it all the time. What I don't understand is: what does the first Leela's proposal mean (marked bold in the dialogue)?

'Lay' can be taken as a slang verb meaning 'to copulate with.' 'Bare' could be understood in this slang context to refer to Fry's potential partner (Leela?) during the 'laying' she was suggesting. 'Laying bare' usually means to make something fully known. Judging by Fry's 'No means no,' he plainly understood her 'offer' and was rejecting her advance.
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MrWonderfulJan 18 '14 at 0:31

2 Answers
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"Lay bare" has a sexual connotation mostly because of the context. It is not typically misunderstood as double entendre.

The Professor first uses the turn of phrase "lay bare" for emphasis. That is appropriate, as the Professor is describing something sublime: The fundamental laws of the universe.

Leela wants Fry. I see two forms of innuendo in her comment. "Lay bare" could mean "have sexual relations with Leela, while she was completely unclothed". The other possibility is more subtle. Leela is making an analogy with the Professor's speech. She is encouraging Fry to act with a similar spirit of exploration and discovery as the Professor is expressing toward cosmology, but toward her. She wants Fry to explore and reveal her in a literal, and sexual manner.

Actually, Fry might understand this quite well, both Leela's first comment about laying bare, and second comment about penetrating the deepest mysteries of quantum physics. That's why he says "No means no". He wasn't interested in "laying bare" Leela a few moments earlier. He responds to her second inquiry, with a second, stronger expression of disinterest.

I don't understand why you say that lay bare is a formal intensifier.
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Stuart CookSep 10 '11 at 12:28

4

@Feral Oink: 'It is not typically misunderstood as double entendre.' From my experience of British English, every utterance has the potential to be understood as a double entendre.
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QubeJun 11 '12 at 12:41

Lay bare is an idiom that means "to reveal or to explain something that was not known or kept secret before." There are other explanations such as "to discover or tell people about something that was not previously known or was previously kept secret."

These are the meanings I could find; I think you can apply them, especially the first one, to your case, saying that Leela meant to tell Fry that she knew something that he could reveal, in the physical sense.

That's what I said too. "Lay her" as in have sex with her, Fry making it an active form. And when bare, like "bare nekkid". So (Lay her) + (bare) = Have sex with all-naked Leela. But I thought that sounded too crude, explicit.
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Ellie KesselmanSep 10 '11 at 13:08

My post is slightly different actually. I think here the idiom is "lay bare", and the relation with "to lay" is secondary. But actually I think that the relation with "having a sexual intercourse" is explained and referred to in the second "sketch", when the "penetrate" word comes into play.
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AlenannoSep 10 '11 at 14:52